“One argument of the Brexiteers is that they want to restore powers and sovereignty to our Parliament – but all three main UK parties officially favour Remain. So it seems paradoxical to give powers back to Parliament to do something it does not want to. There might be pressure on parties to hold a second referendum.”

He added that the public may demand a second referendum after the outcome of Brexit negotiations.

Lord Butler said: “It is also possible that the process of withdrawal would be so awful that people would want to think again, but this would be a major trauma, a major political crisis.

“The Brexiteers are not going to roll over so there would be the mother and father of all fights. There would be a major political crisis in this country.”

There has been speculation that the Commons, which comprises a comfortable majority of pro-Remain MPs, could seek to block Britain leaving the single market if there is a Brexit vote – despite that being the policy of the official Leave campaign.

Last week, Labour’s Stephen Kinnock raised the possibility as he told the BBC MPs would be right to question whether there was a “democratic mandate” for the “devastation and destruction” of the UK’s exports.

Elsewhere, Lord Butler, who was Margaret Thatcher’s principal private secretary before taking the top job in the civil service, predicted David Cameron would have to quit as Prime Minister if there was a Leave vote.

“His position as Prime Minister would be untenable if we vote to leave,” he said.

“Having committed himself so very strongly to the Remain campaign, his authority as PM would have been shattered. I think he would go and fairly quickly.”